03/09/2007 1
Characterisation of PZT thin film micro-actuators using a silicon
micro-force sensor
F. F. C. DUVAL
a, 1
, S. A. WILSON
a
, G. ENSELL
b
, N. M. P. EVANNO
c
, M. G.
CAIN
d
, R. W. WHATMORE
a,2
a
SCHOOL OF INDUSTRIAL AND MANUFACTURING SCIENCE, CRANFIELD
UNIVERSITY, BEDFORDSHIRE, MK43 0AL, UK.
b
INNOS LIMITED, MOUNTBATTEN BUILDING, HIGHFIELD, SOUTHAMPTON,
HAMPSHIRE, SO17 1BJ, UK
c
ROLLS-ROYCE PLC, STRATEGIC RESEARCH CENTRE, SINA-28, PO BOX 31,
DERBY, DE24 8BJ, UK
d
NATIONAL PHYSICAL LABORATORY, HAMPTON ROAD, TEDDINGTON,
MIDDLESEX, TW11 0LW, UK
1
INSTITUT D’ELECTRONIQUE, DE MICROELECTRONIQUE ET DE NANOTECHNOLOGIES,
CITE SCIENTIFIQUE, AVENUE POINCARE, BP 6, 59652 VILLENEUVE D’ASCQ, FRANCE
2
TYNDALL NATIONAL INSTITUTE, LEE MALTINGS, PROSPECT ROW, CORK, IRELAND
Sensors and Actuators A: Physical, Volume 133, Issue 1, 8 January 2007, Pages 35-44.
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Abstract
This paper reports on the measurements of displacement and blocking force of
piezoelectric micro-cantilevers. The free displacement was studied using a surface
profiler and a laser vibrometer. The experimental data were compared with an
analytical model which showed that the PZT thin film has a Young’s modulus of
110GPa and a piezoelectric coefficient d
31,f
of 30pC/N. The blocking force was
investigated by means of a micro-machined silicon force sensor based on the silicon
piezoresistive effect. The generated force was detected by measuring a change in
voltage within a piezoresistors bridge. The sensor was calibrated using a commercial
nano-indenter as a force and displacement standard. Application of the method
showed that a 700μm long micro-cantilever showed a maximum displacement of
800nm and a blocking force of 0.1mN at an actuation voltage of 5V, within
experimental error of the theoretical predictions based on the known piezoelectric and
elastic properties of the PZT film.
Keywords: PZT, cantilevers, vibrometry, force sensors, blocking force.
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I Introduction
Piezoelectric Micro Electro-Mechanical Systems (MEMS) have been studied in many
areas related to precision position control [1], acoustic [2], pressure and gas sensors
[3]. Lead zirconate titanate (PZT) ceramics have been extensively used due to their
superior piezoelectric properties [4] for a wide range of sensors and actuators. For
instance, micro-actuators have been fabricated using a combination of sol-gel derived
PZT and surface micro-machining techniques [5, 6]. The power output is directly
proportional to the thickness of the piezoelectric film, so thicker films are of great
importance. The direct use of bulk PZT ceramics for MEMS devices is not trivial
since it requires expensive and laborious processing to achieve thicknesses below
100µm. The sol-gel technique [7] is a feasible way to deposit PZT films for MEMS
with thicknesses from 1 to 10µm. The method offers good control of the PZT
stoichiometry and is inexpensive. Nevertheless it is limited in the thickness of single
layers that can be grown due to crack occurrence as a result of thermal expansion
mismatch between PZT and silicon substrate [8].
It is well known that thin film properties are significantly lower than the bulk figures
and that films’ properties largely depend on processing conditions. Knowledge of
these properties is of great importance for the modelling of new device designs. Full
experimental characterisation is also needed because modelling cannot always take all
the parameters into account, such as stress gradients, physical imperfections. Intensive
research has been carried out to investigate the properties of piezoelectric cantilever
beams. Due to the small thickness of the beams, the displacement lies in the Å-µm
range. Non-contact techniques such as interferometry [9], atomic force microscopy
(AFM) [10], fiber optic sensor (FOS) [11], laser scanning vibrometer (LSV) [12] have
been successfully used. The latter is particularly suitable to characterise the dynamic
displacement because it measures the velocity of the beam based on the Doppler shift
effect. Another main characteristic of these devices to investigate is the blocking
force, which is not readily achievable using the previously mentioned techniques. It is
common practice to estimate the blocking force knowing the moment of inertia, I and
the maximum displacement (Equation 1) [13].
3
3
3
4.l
.δE.w.t
l
3.E.I.δ
F Equation 1: Expression of the blocking force
where F is the blocking force, E, the Young’s modulus, l, w and t, respectively the
length, width and thickness of the beam, and δ, the displacement. This, however, does
not give a true representation of the blocking force as already shown on macro-scale
piezoelectric actuators [14]. To the best of our knowledge nothing has been yet
reported on the full load vs. displacement characterisation of the blocking force of
micro-scale PZT cantilever beams. This paper presents the fabrication of a micro-
force sensor that was fabricated and calibrated and then used to measure the blocking
force of piezoelectric micro-actuators.
II The micro-force sensor
Principle of force measurement
The force sensor is a silicon beam which includes four piezoresistors arranged in a
Wheatstone bridge, as shown in Figure 1: it is a quarter bridge meaning that only one
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resistor is active, i.e. that on the beam. The active resistor was positioned as close as
possible to the fixed end of the beam, where maximum stress occurs. In order to
measure the force developed by the actuator to be tested, the latter is to be deflected
against the silicon sensor, as shown in Figure 2.
Figure 1: Schematic of the silicon sensor showing the four resistors and the hole for alignment
purpose
Figure 2: Schematic of the interaction between actuator and force sensor
This change in resistance is related to the force produced by the actuator through
calibration curves. Finally, the use of a series of sensors with increasing stiffnesses
(i.e. with different thicknesses) allows the full load vs. displacement curve (Figure 3)
for the test actuator to be constructed.
Figure 3 : Schematic of the full load vs. displacement graph
Piezoresistors design
The p-type piezoresistors were fabricated by ion implanting the silicon surface to
obtain maximum control and hence reproducibility between wafers. The
piezoresistive coefficient and hence, the sensitivity is governed by the dopant
concentration, the orientation of the resistor along the silicon crystallographic axis and
the temperature. The sensitivity is expressed as the change in resistance as shown by
Equation 2 [15].
TTLL
σ.πσ.π
R
ΔR
Equation 2: Change in resistance in a piezoresistor
where R and ΔR are the resistance of the piezoresistor and the change in resistance
respectively, σ
L
and σ
T
, the local stresses occurring in the longitudinal and transversal
directions respectively, π
L
and π
T
, the longitudinal and transversal piezoresistive
coefficients respectively. Using Finite Element Analysis (FEA) (Intellisuite
®
), it has
been found that under specified loading conditions the non-linear influence of
transverse loading on the piezoresistors can be neglected. Equation 2 becomes
LL
σ.π
R
ΔR
with π
L
equal to 72E10
-11
Pa
-1
[15] for silicon p-type resistors.
The piezoresistors were designed to be longer than wide to maximise the effect of
longitudinal stress. The length has to be small to maximise the amount of tension
generated in the resistors. Figure 4 shows the results of an Intellisuite
®
simulation
conducted on a 50μm long piezoresistor (represented as rectangles in Figure 4) to
evaluate how the stress varies when changing the position of the piezoresistor with
respect to the fixed end of the beam. The variation in stress along the length is more
pronounced. At a distance of 100µm from the edge, the stress is only 70% of the
maximum stress. The variation in stress along the width is only less than 1%.
Figure 4: FEA simulations: stress profile for a 400*300*100µm (l*w*t) cantilever when loaded
with 0.3mN as a function of the distance away from the fixed end.
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As imposed by the resolution of photolithography and silicon Deep Reactive Ion
Etching (DRIE), the piezoresistor cannot be placed right at the edge of the cantilever.
Figure 4 also shows that the decrease in stress is less significant if positioning the
resistor 50µm away from the fixed end.
The Johnson noise (J
n
) or thermal noise, as shown by Equation 3, is the thermal
agitation of electrons in a resistor, which gives rise to a random fluctuation in the
voltage across its terminals.
1/2
tn
B)R.T..(4.kJ Equation 3: Expression of Johnson noise
where k
t
is the Boltzmann constant (1.38E-23 J.K
-1
), T, the temperature, R the
resistance and B the bandwidth. Using a resistance of 200kΩ, a temperature of 25°C,
the Johnson noise can be estimated at 0.2μV for a 10Hz bandwidth. It is not
anticipated to be a significant factor for the measurement of the piezoresistive voltage
because the latter is at least 10 orders of magnitude bigger than the Johnson noise
estimated above.
Micro-force sensor design
This part of the design is concerned with the geometrical dimensions of the force
sensors. The width of the cantilevers was fixed at 300µm. The dimensions of the
cantilevers were calculated using Equations 1 and 4.
where
max
σ is the maximum stress, F the force applied to the cantilever.
Silicon cantilevers were designed to measure blocking forces over the range 0.1mN
up to several hundreds of millinewtons. Calculations were carried out with the view of
maximising the maximum stress in the beam, (i.e. making the cantilevers as short and
thick as possible) because the sensitivity is directly proportional to the stress value
(Equation 2). The least stiff silicon beam is 2600*300*50µm and the stiffest is
750*300*200µm in order to cover the range of force to be investigated. The range of
sensors to be made as well as their expected properties are summarised in Table 1.
The change in piezoresistive voltage can be expressed for a quarter-bridge by
Equation 5.
0
.V
R
ΔR
.
4
1
ΔV
where ΔV is the change in voltage and V
0
the input voltage of 10V.
2
max
w.t
6.F.l
σ
Equation 4 : Maximum stress in a cantilever as a function of the
load applied
Equation 5: Change in piezoresistive voltage